Data Collection and Processing

All data used in the regression models are available from Medalie and Stagnitta (2023). Most data were collected at a monthly time step from July 2014 to June 2021, except for data during drought periods which were available at a weekly time step and were aggregated to monthly values. The spatial scale of the variables differs. The water use data provided in Medalie and Stagnitta (2023) cover water use in the service area for Providence Water (fig. 1). For context, in 2021, Providence Water directly served about 310,600 people, or about 29 percent of the population of the State (1,059,000); an additional 299,700 people (28 percent of the population) used water from public water systems that were wholesale customers of Providence Water.

Climate data were acquired from the National Climatic Data Center weather station in Warwick, Rhode Island (about 7 miles south of Providence), at the T.F. Green State Airport station (fig. 1; National Centers for Environmental Information, 2021a, b14). Monthly economic variables were retrieved from the Federal Reserve Economic Data (FRED) System (Federal Reserve Bank of St. Louis, 2021) at the spatial scale of the State of Rhode Island.

Water Use Variables

Beginning in 2012, all large public suppliers (defined as those who withdraw or purchase at least 50 million gallons per year) in Rhode Island have been required to submit annual reports to the Rhode Island Water Resources Board, including information on withdrawals, sales volumes, and distribution of water to customer categories of single-family residential, multifamily residential, commercial, and industrial. Providence Water furnishes annual reports with data at a monthly time step (some other water suppliers in Rhode Island furnish annual reports at a quarterly time step). Water distribution information is furnished as both gallons and number of customers for each category of water use.

Data that Providence Water reported as water delivered to two to five families is called “multifamily residential water use” for the purposes of this report. Water delivered by Providence Water to two to five families averaged 70 percent of total deliveries to multifamily customers during 2014–21, with other types of multifamily customers being apartments and residential condominiums.

Water use that Providence Water reported as commercial I and commercial II are added together and called “commercial water use” for the purposes of this report. Providence Water distinguishes between commercial I and II water use based on the property’s tax assessment value (assessed values are less than $500,000 and greater than $500,000 for commercial I and II, respectively) but both categories include facilities such as hotels, restaurants, retail stores, and office buildings. The categories of commercial I and II, as defined by Providence Water, do not include hospitals, schools, and municipal or State properties, which are reported as separate types of commercial entities. Water delivered by Providence Water to commercial I and II customers averaged 51 percent of total deliveries to all commercial customers from 2014 to 2021. Industrial water use is defined as water used for fabrication, processing, washing, and cooling (Dieter and others, 2018).

Initial data processing included plotting monthly single-family and multifamily residential, commercial, and industrial delivery data to look for missing values, outliers, and unexpected patterns. Because monthly data from Providence Water from July 2011 through June 2021 showed that data became noticeably more consistent (within an annual cycle) starting in July 2014, the study period was set to start in July 2014. Missing values were requested and received from Providence Water. Fluctuations in delivery volumes were seen, as expected, from month to month (fig. 2) and could reflect actual variability in delivery, inconsistent meter reading schedules, or errors in reporting or meters. Providence Water attributes large monthly anomalies primarily to the fact that meters are not always read on the same date every month (Peter LePage, Providence Water, written commun., December 21, 2021). To reduce month-to-month fluctuations from variations in meter reading intervals, the 3-month moving mean was calculated and used for each water use dependent variable.

Seasonal Indicator Variables

Water deliveries by Providence Water to single-family residential, multifamily residential, and commercial customers displayed a distinct seasonal pattern, with the greatest volume of water being used in summer months, and the least volume in winter months (fig. 3). This pattern is common in temperate areas like Rhode Island because, while indoor water use typically does not change dramatically throughout the year, outdoor water use (for activities such as watering lawns and gardens, filling pools, and washing cars) is greater during the summer than other times of the year (Ahmed and others, 2020). These seasonal patterns reflect differences in water deliveries through the seasons rather than differences in the number of customers in Providence, which tend to remain fairly constant throughout the year, although some areas in Rhode Island, generally outside of Providence, have large summer tourist populations. Although the seasonal pattern for industrial users (figs. 2D and 3D) was less marked than for the other water use categories, higher volumes of water were used in the summer than in other months of the year.

To address seasonal differences in water use, two seasonal binary indicator variables were created for the regression models (table 2). To indicate high water use in summer for July through September, the high water use variable is assigned “1,” and other months were assigned “0.” To indicate low water use in winter for December through May, the low water use variable is assigned “1,” and other months were assigned “0.” Transitional months (June, October, and November) are not assigned a separate indicator variable (Helsel and others, 2020).

Table 2.    

Definition of seasonal indicator variables and assignment of binary values for modeling water use in Providence, Rhode Island.

Table 2.    Definition of seasonal indicator variables and assignment of binary values for modeling water use in Providence, Rhode Island.

Seasonal variable	Value of 1	Value of 0
High water use (HighWU)	July, August, September	All other months
Low water use (LowWU)	December, January, February, March, April, May	All other months

Regression Analysis

The regsubsets function of the R leaps (version 3) software package (Lumley, 2020) was used to perform an exhaustive search for the best subsets of independent variables to predict single-family residential per capita, multifamily residential per connection, commercial per connection, and industrial per connection water demand with each dependent variable expressed as the 3-month rolling mean, using ordinary least squares linear regression (Miller, 2019; Lumley, 20207). The variables are grouped into climatic, economic, and binary categories, as follows.

User-specified input to the regsubsets function includes the maximum number of independent variables to allow in the regression and the number of models to include in the output for each specified number of independent variables. For this study, 10 was used as the maximum number of independent variables and 5 or 6 as the number of models to include in the output for each water use category. Models with too many explanatory variables are likely overly complex—they are less likely to find significance in hypothesis tests and they increase the width of confidence intervals (Helsel and others, 2020). The output from regsubsets is a list of model coefficients for each of the 5 or 6 best models for models with 1 to 10 explanatory variables. Regsubsets optimizes regression models based on the diagnostic statistics adjusted coefficient of determination R², Mallows’s Cp, and the Bayesian information criterion (BIC; Lumley, 2020).

The output from regsubsets narrows the universe of combinations of independent variables that can be used to build the regression model. The model_water_use_functions.R script (Medalie and Stagnitta, 2023) has a custom function (best_regsub_out) that includes additional diagnostic statistics (predictive R², prediction error sum of squares [PRESS], and variance inflation factor [VIF]) to evaluate model performance. The best models, determined using the output from regsubsets and best_regsub_out function, minimize Mallows’ Cp, PRESS, and VIF and maximize adjusted R² and predictive R² (Helsel and others, 2020). Two regression model error metrics—standard error and normalized root mean square error—also are provided.

Potential regression models were further assessed by checking that all independent variables were significant (p-values are less than 0.05) and by analyzing diagnostic plots to ensure that all assumption of linear regression were met (Helsel and others, 2020). Independent variables were compared against the given dependent variable for credibility. Although independent variables identified in the regsubsets output did not always seem intuitively related to the dependent variables, each relation was considered for plausibility on a case-by-case basis, even if it were not causal.

Residual diagnostic plots such as the model residuals versus fitted values and the normal probability plot (Q–Q plot) of standardized residuals were used to ensure that the model was normally distributed, the variance of residuals was constant, and the residuals were nonbiased. In addition, plots for residuals versus leverage and Cook’s distance helped to identify outliers in independent variables and observations with large influence, respectively. Partial-residual plots, which show nonlinearities within each individual explanatory variable, were used to check whether any of the explanatory variables needed to be transformed.

A sensitivity analysis (Mishra, 2009) was performed to assess the relative influence of each explanatory variable identified in the single-family residential model, which accounts for the largest category of water use by Providence Water. For the sensitivity analysis, the single-family residential regression model was re-run after centering (standardized to have a mean of 0 and a standard deviation of 1) all explanatory variables, including the binary variables. The standardized regression model explains the mean change of single-family residential per capita water use given a 1 standard deviation shift (positive or negative) in each independent variable. The explanatory variables with the highest influence have the largest coefficients (positive or negative). The sensitivity analysis helped identify the explanatory variables that had the largest influence on single-family residential water use.

Single-Family Residential Model

Single-family residential water use had the most consistent seasonal variation of the four water use categories and constitutes by far the largest customer base within the Providence Water service area (approximately 48,000 connections). This large customer base diminishes the effect of customers who use unusually large or small volumes of water. The highly influential seasonal high and low water use variables perform exceptionally well at modeling the consistent pattern of high water use in the summer and low water use in the winter (fig. 4A).

Two climatic variables in the single-family residential model—minimum temperature and the drought index—have a positive relation to single-family residential water use. Summer, when temperatures and the likelihood of drought are the highest, is the season with the highest single-family residential water use. The summer peaks in single-family residential water use are attributed to outdoor uses, such as gardening and irrigation, pool filling, car washing, and other outdoor uses (Water Research Foundation, 2016). The droughts of 2016 and 2020 included record-breaking temperatures and extended periods of limited precipitation that coincided with spikes in water use (fig. 4A).

Before the COVID–19 pandemic, economic activity, as measured by the CEAI (fig. 5), was increasing in Rhode Island at the same time that single-family residential water use was decreasing (fig. 4A). In contrast, seasonally adjusted total private employees within Rhode Island and single-family residential water use are directly related (table 3). Perhaps this latter pattern reflects the large loss of jobs in restaurants, hotels, automotive repair, and other personal services resulting from COVID–19 that had not fully recovered by the end of the study period in July 2021 (State of Rhode Island Department of Revenue, 2021).

The effects of the COVID–19 pandemic on the economy in Rhode Island displayed two distinct patterns that were consistent with findings across the country: (1) total retail trade decreased initially but recovered to slightly above prepandemic levels by the end of 2020 and (2) service sectors like restaurants and hotels were among the most severely affected industries of the pandemic and did not recover to prepandemic levels by the end of 2020 (State of Rhode Island Department of Revenue, 2021). Coinciding with the spring and summer seasons of peak water use (fig. 3A), total retail trade surpassed pre-pandemic levels by May 2020 and services like restaurants, hotels, auto repair, and other personal services recovered about half of the initial losses by July 2020 (State of Rhode Island Department of Revenue, 2021).

To assess the influence of economic variables on single-family residential water use under typical conditions, a regression model was constructed for the period before the onset of the pandemic (July 2014 to February 2020); this regression model was outside the scope of this study and was not included in this report. Using the same regression model diagnostic statistics shown in table 4, the best of these models included the same economic variables (CEAI and number of private employees) that were included in the model that used data for the entire study period. This exercise demonstrated the robustness of these economic variables for estimating single-family residential water use.

Multifamily Residential Model

The multifamily residential model includes the same two economic variables and seasonal water use variables as the single-family residential model; the model also includes the climate variable snowfall. Total monthly snowfall has a positive relation to multifamily residential water use. Although multifamily residential water use was lower in winter than summer, winter water use was typically higher in January and February, when monthly snowfall totals are largest compared with other winter months (fig. 4B). Total monthly snowfall showed a slight downward trend across the 7-year study period, similar to the overall downward trend in winter multifamily residential water use (fig. 2B, green dots).

As in the single-family residential model, CEAI is inversely related to multifamily residential water use (table 3). The number of private employees in Rhode Island, which reflects the sharp recovery of jobs after April 2020, has a direct relation to multifamily residential water use. Although the economic variable number of private employees is significant in both residential models, the seasonally adjusted version is in the single-family residential model, whereas the unadjusted version is in the multifamily residential model. This appears to show that seasonal fluctuations in jobs in Rhode Island (higher during summer than winter) play a larger role in influencing single-family residential water use than in multifamily residential water use.

The seasonal pattern displayed by multifamily residential water use is not as prominent as the seasonal pattern observed for single-family residential and commercial water use customers (fig. 2A and B). Indoor water use in multifamily residential buildings is greater than in single-family residential buildings because more people reside in a multifamily building, but multifamily residences use less water outdoors than single-family residences and therefore use less water overall (Ahmed and others, 2020). One hypothesis is that multifamily homes have smaller lawn areas on a per-customer basis, leading to less outdoor water use than single-family residences. Indoor water use is steadier throughout the year and less influenced by seasonal changes than outdoor water use. However, multifamily residential water use does have a moderate seasonal pattern that is adequately captured by the high and low water use variables in the regression model.

Commercial Model

The commercial water use model includes no climatic variables, one economic variable, the COVID–19 pandemic variable, and the high and low water-use seasonal variables. Economic activity represented by CEAI appears to be coincidental but is not necessarily causal to commercial water use during the study period. Between July 2014 and March 2020, commercial water use shows a downward monotonic trend (fig. 4C), whereas the CEAI shows an upward monotonic trend (fig. 5). When the COVID–19 pandemic began, commercial water use and the CEIA appeared to respond similarly; both quickly dropped, followed by a return (or near return) to pre-COVID–19 trajectories (Medalie and Stagnitta, 2023).

The COVID–19 pandemic had a significant effect on both commercial water use (table 3) and the CEAI (fig. 5). Rhode Island Executive Order 20–13, issued by the Governor on March 28, 2020, directed the closure of all noncritical retail businesses (Raimondo, 2020). Other types of commercial entities, such as hotels and office buildings, also were affected by COVID–19-related travel restrictions and stay-at-home orders, which resulted in a sharp increase in teleworking in many industries. Thus, the COVID–19 pandemic and the resulting executive order had the immediate effect of severely reducing commercial water use (Medalie and Stagnitta, 2023).

Both seasonal indicator variables, HighWU and LowWU, are significant in the commercial model, indicating the importance of seasonal fluctuations in water use (figs. 2C and 3C). Restaurants and hotels in Providence are busiest during summer and least busy during winter, driving seasonal commercial water use patterns (Champion Traveler, 2022). In addition, landscaping and commercial cooling systems that use water increase summer water needs at many types of commercial facilities compared with other times of the year (U.S. Environmental Protection Agency, 2021).

Industrial Model

Industrial water use was relatively constant on an annual basis between 2014 and 2018 and then decreased between 2019 and 2021 (fig. 2D). That the industrial water use model was less accurate than the other water use models is likely related to two factors: (1) water deliveries to the industrial sector are more irregular with a greater range of values (Medalie and Stagnitta, 2023), and (2) industrial water use has a less distinct seasonal pattern (fig. 2), which means that climate data are less effective predictors for modeling. Although each of the other three models include both HighWU and LowWU as explanatory variables, the industrial model includes only LowWU because deliveries during the summer and transition seasons were not distinguishable from one another. Like the single-family residential model, the industrial model includes the average monthly minimum temperature, which gives additional explanatory power to the seasonal component of water use. Although manufacturing activities in industries generally are less affected by seasonal differences in tourism and related factors that increase commercial water use during the summer, industrial water use is somewhat higher during the summer than the rest of the year because of landscaping and cooling system water use (fig. 3D).

The inclusion of the two seasonal variables, average monthly minimum temperature and LowWU, in the industrial water use model might also reflect manufacturing patterns of the largest industrial water user, Pepsi Bottling Group in Cranston, which receives water from Providence Water. By a wide margin, Pepsi Bottling is the largest industrial water user in the Providence Water service area (the 2019 reported water deliveries to Pepsi Bottling Group were nearly double the reported deliveries to the next largest industrial user). As such, Pepsi Bottling might have a disproportionate influence on overall industrial water use, given the small number of industrial customers of Providence Water—the median number of industrial customers is 47—compared with about 4,300 commercial customers. The 2020 PepsiCo annual report indicates that sales have a seasonal component and are generally highest in the third quarter (defined by PepsiCo as June, July, and August) and lowest in the first quarter (December, January, and February; PepsiCo, Inc., 2021). To meet demand from sales, manufacturing at Pepsi is likely also highest in the summer months and lowest in the winter months, consistent with the overall seasonal pattern of industrial water use.

The industrial water use model includes two economic variables—imports and jobs in construction—and does not include other economic variables that might have been expected: jobs in manufacturing and CEAI. Jobs in manufacturing were highest in 2014 through 2015, then decreased by about 2 percent from 2016 through 2018, followed by a decrease of another 1 percent in 2019, before a sharp decrease in March 2020 when the COVID–19 pandemic began (Medalie and Stagnitta, 2023). The plunge was followed by steady recovery. That pattern bore little relation to industrial water use during the same period (fig. 2D). Although imports and jobs in construction are not directly related to manufacturing or industrial water use, they are indicators of general economic activity and might be affected by some of the same drivers. Imports increased between about 2014 and 2019 and then decreased between 2019 and 2021 (Medalie and Stagnitta, 2023); this latter period coincides with a decrease in industrial water use (figs. 2D and 4D). In contrast, the increase in jobs in construction remained steady throughout the study period (Medalie and Stagnitta, 2023), resulting in an inverse relation with industrial water use. The general economic indicator variable CEAI may have been superseded in significance in the industrial model by the inclusion of the COVID–19 binary variable—both variables capture the large step change in many activities in March 2019.

Application of Models

An important finding from this study is that different types of water uses were attributable to different factors. The regression models developed for this study can help to inform future modeling efforts to forecast short-term and long-term water use in Rhode Island. These models are intended to provide a basic understanding of water use in the State and can be improved or modified to address specific questions or scenarios. Examples of potential model applications include (1) predictions of the influence of climate change on seasonal and long-term water use patterns, (2) the generation of water use projections from public-water suppliers who are considering merging, and (3) modeling of other categories of water use, such as hospitals, restaurants or schools, or other categories of commercial water use not included in Providence Water’s definitions of commercial I and II. More sophisticated approaches to modeling water demand that use various machine learning techniques might offer some benefits compared with the traditional regression approach used in this study, such as the ability to use complex data from different statistical distributions, and the ability to incorporate nonlinear relationships between variables (Villarin and Rodriguez-Galiano, 2019). Models developed in this study suggest that water demand is readily predictable and can serve as starting points for developing new regression models for other public-water suppliers in Rhode Island. The finding that the COVID–19 binary variable was significant in the commercial and industrial models shows that a highly influential event such as a pandemic can be adequately captured and modeled and suggests that this type of model is likely to be adept at capturing other similarly large-scale events or disturbances in the future.

This work also complements a parallel effort by the Rhode Island Water Resources Board (2022), in collaboration with the University of Rhode Island and the Rhode Island Geological Survey, to estimate water withdrawals for small public-water suppliers that are not required to report withdrawal and use information to the State. Taken together, these efforts will improve accounting of all water withdrawals and use in Rhode Island.